# Rational Roots

• Oct 22nd 2006, 08:10 AM
JimmyT
Rational Roots
Just quick:

I have (2x^4)+(4x^3)-(5x^2)-5x+2.
The only possible rational roots by the Rational Root Test are 1,-1,2,-2,.5,-.5.
The only one that works out of these is -1. Could someone just check this for me?

Jimmy
• Oct 22nd 2006, 08:29 AM
topsquark
Quote:

Originally Posted by JimmyT
Just quick:

I have (2x^4)+(4x^3)-(5x^2)-5x+2.
The only possible rational roots by the Rational Root Test are 1,-1,2,-2,.5,-.5.
The only one that works out of these is -1. Could someone just check this for me?

Jimmy

I agree. Good work!

You can always check these by division as well. You should be able to divide $2x^4+4x^3-5x^2-5x+2$ by x - (-1) either by long or synthetic division to find:
$2x^4+4x^3-5x^2-5x+2 = (x+1)(2x^3+2x^2-7x+2)$
confirming that there is no remainder.

-Dan